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THERMOCHEMISTRY OF BINARY HALIDE MIXTURES
Thermochemistry of Charge-Unsymmetrical Binary Fused Halide Systems. 11. Mixtures of Magnesium Chloride with the Alkali Chlorides and with Silver Chloride
by 0. J. Kleppa and F. G. McCarty Institute for the S t u d y of Metals and Department of Chemistry, T h e Unicersity of Chicago, Chicago, Illinois (Received h'oaember 8, 1965)
60637
The integral enthalpies of mixing of the liquid mixtures of magnesium chloride with the alkali chlorides and with silver chloride have been determined calorimetrically. The magnesium chloride-silver chloride system is slightly endothermic, while the alkali chloride systems are all exothermic, the negative enthalpy of mixing increasing sharply in the sequence Li < Ka < K < Rb < Cs. For the mixtures of magnesium chloride with sodium, potassium, rubidium, and cesium chloride, the enthalpy of mixing changes linearly with the parameter 812 = (dl - d z ) / d l d z ; dl and dz are the sunis of the ionic radii of the two solution partners. This is consistent with the conformal solution theory of Davis for charge-unsymmetrical systems. The integral enthalpy data are discussed with respect to the asymmetry of the interaction parameter (AH"/X(l - X)) and the deviations of this parameter from a linear dependence on composition. Relative partial enthalpies for magnesium chloride have been derived and have been compared with corresponding excess free energies reported in the literature. The new enthalpy data are interpreted to support the view, originally advanced by Flood and Urnes, that the alkali chloride-magnesium chloride mixtures contain the complex anionic species RIgC142-. The stability of this species depends strongly on the alkali cation present, and increases from lithium to cesium.
Introduction Among the binary mixtures formed by fused salts, the simplest ones have two solution partners of identical charge structure containing a common ion. The common ion may be an anion, as in NaCl-KCl, or a cation, as in NaBr-NaC1. I n recent communications from this laboratory, the results of a comprehensive thermochemical investigation of binary halide mixtures of the former type have been reported.'r2 Somewhat more complex in character are mixed systems in which the two solution partners have different charge structures while they still contain a common ion. Among these systems, particular interest is attached to the mixtures of the divalent halides with the corresponding alkali halides. We have recently reported the results of a thermochemical study of the lead chloride-alkali chloride liquid mix-
t u r e ~ . I~n the present communication, our investigation of this type of solution system is extended to the mixtures of magnesium chloride with the alkali chlorides and with silver chloride. The magnesium chloride-alkali chloride systems have in the past attracted considerable attention due to the possible existence of the complex h!tgC142- in the melts. This possibility has been discussed in particular by Flood, Fpjrland, and co-workers, and very recently by Neil, et aL6 The data reported in the present work 4 3 5
(1) L. S. Hersh and 0. J. Kleppa, J . Chem. Phys., 42, 1309 (1965). (2) LI S. Hersh, A. Navrotsky, and 0. J. Kleppa, ibid., 42, 3752 (1965). (3) F. G. McCarty and 0. J. Kleppa, J. P h y s . Chem., 68, 3846 (1964). (4) H.Flood and S.Urnes, Z . Elektrochem., 59, 834 (1955). (5) T. Fgkland in "Fused Salts," B. R. Sundheim, Ed., McGrawHill Book Co., Inc., New York, N. Y.,1964.
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permit a look a t this problem in the light of the enthalpy of mixing. From the point of view of the present investigation, it is of particular interest that several of the magnesium chloride-alkali chloride systems also have been studied by means of emf formation c e l l ~ . ~ This J method, which was pioneered by Hildebrand and co-workers,* in principle may provide information on the enthalpy and entropy of mixing as well as on the free energy. However, it is generally recognized that the enthalpy and entropy data derived in this way often are of doubtful value. This certainly holds for the enthalpies and entropies for t.he magnesium chloride-alkali chloride systems given by Markov, et a1.' On the other hand, free energies from emf work tend to be more accurate than the derived enthalpy and entropy data. I n the present investigation, such free energy data will be compared with the corresponding enthalpies. This combination offers the best prospect of obtaining reliable information on the entropy of mixing.
Experimental Procedures and Materials The calorimeter used in the present work is in many respects similar to one for work up to 500" which is described in some detail in the l i t e r a t ~ r e . ~The modifications necessary for operation a t temperatures up to about 800" have been discussed elsewhere.' The calorimetric work reported here was carried out in the temperature range 730-810". All experiments were of the simple liquid-liquid mixing type. They were performed in an atmosphere of dry pure nitrogen, using fused silica containers and break-off t u b s . g Under the conditions of our experiments, the melt attacked the silica containers only slightly, and all containers could be used several times. Calibration was by the gold-drop method, based on the heat content equation for pure gold given by Kelley.l0 A small correction was applied for the pickup of heat by the falling gold wire.' The magnesium chloride was prepared by removing the water from Mallinckrodt analytical reagent MgClz.6Hz0. This salt was first heated very slowly to about 250" under rotary-pump vacuum. After the greater part of the water had been driven off in this manner, the salt was slowly brought up to the melting point and was melted down in a stream of dry HCI-Nz mixture. The final product consisted of an agglomeration of quite coarse crystals of anhydrous MgC12. The product was neutral with respect to phenolphthalein when dissolved in water. I n the form of small chunks it could be handled outside a drybox for short periods of time without gain in weight. The alkali The Journal of Physical Chemistry
I
I
I
I I I
0.2
0.4
I
I 06
I
I 08
I
M ~ c , ~
Mole Fmction, Xuoclp
Figure 1. Molar enthalpies of mixing ( A H M ) in liquid mixtures of magnesium chloride with silver chloride and with the alkali chlorides.
chlorides and silver chlorides were of the same origin and quality as the salts used in our earlier work.'v2
Results and Discussion All experimental results obtained in the course of the present investigation are recorded in Table I. The columns in this table are: (1) mole fraction of magnesium chloride in the liquid mixture, (2) total number of moles in each experiment, and (3) molar enthalpy of mixing, AHM. The product of the numbers in columns 2 and 3 will give the enthalpy of mixing actually observed in each individual experiment. We give in Figure 1 a graph of AH* vs. mole fraction for all the mixtures investigated. I n order to discuss ~~
(6) D. E. Neil, H. M. Clark, and R. H. Wiswall, J . Chem. Eng. Data, 10,23 (1965). (7) B- F. Markov. I. K. Delimarskii, and I. D. Panchenko, Zh. Fiz. Khim.,29, 51 (1955). (8) J. H.Hildebrand and E. J. Salstrom, J. Am. Chem. SOC.,54,4257 (1932). (9) 0.J. Kleppa, J . Phye. Chem., 64, 1937 (1960). (10) K. K. Kelley, U. 9. Bureau of Mines Bulletin 584, U. S. Government Printing Office, Washington, D.C., 1960.
THERMOCHEMISTRY OF
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BINARY HALIDEl/IIXTURES
Table I : Molar Enthalpies of hlixing (AHM)in Liquid Mixtures of Magnesium Chloride with Silver Chloride and with the Alkali Chlorides Composition xMgC12
AHM,
Total moles
0.1714 0.2589 0.3789 0.4599 0.6200 0.6871 0.8095 0.8264
MgC12-AgC1 a t 730" 0.1250 0.1418 0.1668 0.1947 0.1686 0.0917 0.1164 0.1268
0.0828 0.0875 0.2097 0.2164 0.3783 0.4540 0.5962 0.7087 0.7422 0.8243 0.8938
MgClz-LiC1 a t 730" 0.1305 0.1293 0.1514 0.1202 0,1520 0.1725 0.1757 0.0811 0.2117 0.1270 0.1758
0.0774 0.1353 0.2127 0.3361 0.3808 0.4868 0.6482 0.6860 0.7983 0.8834
MgC12-NaC1 a t 810" 0.2443 0.1399 0.2863 0.1822 0.2489 0.2168 0.1462 0.2353 0.1322 0.1827
0.0608 0.1059 0.2047
MgC12-KC1 a t 800" 0.1728 0.1502 0.2041
AH^,
(:omposition,
cal/mole
XMgCli
Total moles
cal/mole
49 65 76 80 87 85 75 81
0.2602 0.3524 0.4495 0.5300 0.6230 0.6577 0.8147 0.8816 0.9415
MgCl2-KCl a t 800" 0.1815 0.1636 0.1749 0.1088 0.1262 0.1630 0.1935 0.1216 0.1674
-3105 -3735 - 3735 - 3587 -3147 - 3062 - 2006 - 1348 -721
0.0551 0.0934 0.1336 0.2001 0.2453 0.2923 0.3160 0.3365 0.3858 0.4700 0.5097 0.6406 0.7610 0.8609
MgC12-RbC1 a t 730" 0.1046 0.1121 0.1180 0.1048 0.1310 0.1436 0.1495 0.0750 0.1365 0.0939 0.1555 0.1640 0.1042 0.1220
0.0602 0.1063 0.1878 0.1917 0.2293 0.3205 0.4236 0.5261 0.6179 0.7162 0.8737 0.8980
MgC12-CsCl a t 730" 0.0950 0.0997 0.0586 0.1105 0.0929 0.1311 0.1242 0.1004 0.1017 0.1466 0.0720 0.1169
- 182 - 189 - 380 - 395 -444 -469 - 370 -255 -215
- 134 - 70 - 540 -918
- 1339 - 1773 - 1870 - 1839 - 1510 - 1404 - 956 - 586
-792 - 1342 - 2497
in detail the variation of AH" from system to system we give also in Figure 2 a corresponding plot of the experimental values of the interaction parameter, X = AH"/X(l- X ) . Note first the systematic dependence of X on the size of the alkali metal cation, with values ranging from about -2 kcal/mole for lithium-magnesium to -20 kcal/mole for cesium-magnesium chloride. A similar trend has frequently been noted in the thermodynamic behavior of simple charge-unsymmetrical fused salt mixtures, Qualitatively, this trend may be rationalized in terms of the competition between the two cations for the common anion. I n this competition
-820 - 1394 - 1959 -2915 -3392 - 3909 - 4241 -4338 - 4426 -4423 4345 3768 - 2974 - 1946
-
- 1017 - 1849 -3112 -3192 -3862 -4984 - 5288 - 4823 - 4466 - 3864 -2166 - 1798
the cation is aided by a small size, a high charge, and a high polarizability. I n view of the similarity of the ionic radii of sodium and silver, the latter point explains the striking difference between the moderately exothermic sodium-magnesium chloride system and the slightly endothermic, in fact nearly ideal, silvermagnesium chloride. Recently, a modified conformal solution theory for the heats of mixing in charge-unsymmetrical fused salt syst,ems was developed by Davis,ll on the basis of the model ionic melt of Reiss, et aL12 Since the (11) H. T. Davis, J . Chem. Phys., 41, 2761 (1964).
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0. J. KLEPPAAND F. G. MCCARTY
L===d
-13.0
I-WI
-14.0
-1.0 -15.0
-
e -7 Z
-2.0
-16.0
< (Y
-3.0 -17.0
" 0
Y
Y
-
-4.0 2
-7
-18.0
I
X
%
-5.0 -19.0
S .
I
-6.0
f D
a
-20.0
-7.0
-2LO
-8.0
-220
Figure 3. Dependence of the interaction parameter on the quantity 612 = ( d l - d2)/dld2.
studied in previous work. In view of this observation, we may for the alkali chloride-magnesium chloride systems (again excepting lithium-magnesium) w i t e Figure 2. Inieraction parameters (X = AHM/X(l - X))in liquid mixtures of magnesium chloride with silver the empirical relation, X = K(X)612,where the coefchloride and with the alkali chlorides. ficient K ( X ) , although it varies significantly with composition, is of the order of - 150 kcal A/mole. Figure 2 indicates that the variation of the interacDavis theory does not permit an explicit evaluation of tion parameter within any one system involves two the enthalpy of mixing for any chosen binary system, prominent features : (a) energetic asymmetry; generwe shall not discuss it in detail. ally X takes on values in the magnesium chloride-rich However, according to Davis the interaction paramregion which are different from those in the alkali eter, in a family of related systems such as that conchloride-rich region (XAC~ XI~~C,~); (b) departures sidered in the present work, should to a first approxifrom linearity. This is particularly pronounced near mation depend linearly on the parameter 612 = (d1 = 0.33. Thus X A ~ J I ~ often C ~ ~ differs very sigX~1pc1~ dz)/dlclz, where cll and dz are the interionic distances I(2/dX.h~l (1/8)X~lg~~n1. nificantly from which characterize the two salts. The linear relation The Davis theory for cha~ge-unsynz?izetI.icalmixtures between X and 612 has been found to hold fairly well has not been developed to a point where it allows for the alkaline earth nitrate-alkali nitrates," and quantitative predictions to be made regarding eneralso, with the exception of the lead-lithium system, getic asymmetry. On the other hand, in evaluating for the lead chloride-alkali chloride^.^ the higher order terms in the theory of Reiss, et aZ.,I2 I n Figure 3 we give a plot of X against 612 for the confor charge-symmetrical systems, Blander13 found that sidered alkali chloride-magnesium chloride mixtures. this theory predicts contributions to the energetic Since X varies with composition, we have selected for asymmetry which depend on the third power of 612. consideration the values at XbfpCl, = 0.33. The figure Hersh and Kleppa' found evidence for this kind of decontains both the actual experimental values ( X A ~ M ~ C ~ J pendence in their study of the binary alkali halides. and those obt,ained by linear interpolation of the two Without any attempt at theoretical justification we With the terminal values [('/3)XACl 4- ( 1 / 3 ) h I & 1 2 ] . have tested this relation also for the considered alkali obvious exception of the lithium-magnesium system, chloride-magnesium chloride systems in Figure 4. the predicted linear dependence of X on 612 clearly is confirmed. It is particularly interesting that the lines (12) H. Reiss, J. L. Kat?;, and 0. J. Kleppa, J . Chem. Phys., 36, 144 drawn through the experimental points in Figure 3 (1962). extrapolate to 0 at 612 = 0. In this respect t h e alkali (13) M. Blander, ibid., 37, 172 (1962). Actually, the predicted dz). For moderate asymmetries are related to 6 = (di - d z ) / ( d i chloride-magnesium &loride systems appear to be differences in ionic size the choice between the parameters 6 and 612 simpler than the charge-unsymmetrical systems is not significant. mole fraction.XMICll
+
.
I
+
The Journal of Physical Chemistry
1253
THERMOCHEMISTRY OF BIKARY HALIDEA~IXTURES
I
I
x -2.0 1 . 0 I
0
I
-0.5
I
-1.0
I
-1.5
1
-2.0
1 0 ~ ~ 8, ,%-3 ; Figure 4. Dependence of the energetic asymmetry on the parameter 613 = (di - d2)/dld2.
From an empirical point of view it is apparent that the energetic asymmetry indeed varies linearly with ~12~. In the previously studied binary alkali halide and nitrate systems, departures of X from a linear dependence on composition are small. Also, such departures, when present, are symmetrical in the mole fractions of the two components. Among the systems studied the largest departure was found in lithiumcesium chloride, with a value of about -500 cal a t the 50 :50 composition. In these charge-symmetrical systems the magnitude of the deviation of X from linearity correlates with the square of the interaction parameter. This was attributed by Kleppa and Hersh14 to short-range order in the cation “sublattice.” The observed dependence on X 2 is consistent with quasichemical theory.15 I n charge-unsymmetrical systems the nature of the deviation of X from linearity clearly has a different character. For example, in our recent work on the lead chloride-alkali chlorides we found the deviations to be somewhat more pronounced than in the binary alkali halides. Also, the deviations are unsymmetrical in the mole fractions of the two components. For cesium chloride-lead chloride, which was the only system with a nonlinear X studied over the full range of liquid compositions, the maximum negative deviation of X from linearity is about 1 kcal and occurs somewhere between 65 and 80 mole % cesium chloride. In the considered mixtures involving magnesium chloride, the magnitude of the deviation is still greater. For example, the three systems containing potassium, rubidium, and cesium chloride all have sharp dips in X near Xarpclr := 0.33. For the sodium- and lithium contairling systems the composition Of maximum deviation cannot be pin-pointed as readily.
Figure 5. Dependence of the deviation of the interaction parameter a t XMgCl, = 0.33 from linearity on its magnitude.
However, even in these cases it is evident that the deviation is unsymmetrical in the mole fractions of the two components and that the maximum deviation occurs on the alkali chloride-rich side. I n the systems under consideration we also find a different relationship between the deviation from linearity and the magnitude of X. This is illustrated in Figure 5, which gives a plot of X A ~ M ~ C , ,- [ ( 2 / 3 ) . It is apXACl (‘/3)XMgC12] us. ‘/2(XAC1 XhfgCh). parent that a linear dependence is indicated. In our earlier work on the lead chloride-alkali chloride mixtures, the unsymmetrical character of the deviat,ion from linearity was interpreted to indicate the formation of complex species in the melt. However, the uncertainty in the location of the maximum deviation ruled out any attempt to draw firm conclusions regarding the most stable anionic configuration. I n the considered systems this uncertainty in large measure is removed. I n view of Figure 2 there can be little doubt that R!IgC142- must be the most prominent complex species in the potassium, rubidium, and cesium chloride melts. By inference, we conclude that this species is of considerable importance also in sodium chloride-magnesium chloride, and to a lesser extent even in lithium chloride-magnesium chloride. These conclusions will be the subject of further discussion below. Partial Molal Quantities. The new data reported above are all integral enthalpies. While no attempt was made in the present work to obtain partial enthalpies by direct measurements, the experimental
+
+
(14) 0. J. Kleppa and L. S. Hersh, J. Chem. Phgs., 34, 351 (1961). (15) E. A. Guggenheim, “Mixtures,?7Oxford University press, New York, N. Y., 1952.
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0. J. KLEPPAAND F. G. MCCARTY
1254
X Mc,2=0.33
-18.0 -I8''
-I6,O
t -10.0
-17.1
,Present I w0rk,730-810"C
,
- 16.0
-x-
t
-8'ol diagrc
-6.0
I
AC I Mole Fraction, XK? Figure 6. Partial excess enthalpies and partial free energies of magnesium chloride in its liquid mixtures with the alkali chlorides.
results on the whole are sufficiently precise and extensive to allow quite reliable smoothed curves to be drawn. From a large-scale version of Figure 1, fairly reliable relative partial enthalpies were derived by the method of intercepts. The resulting curves for magnesium chloride in its mixtures with the alkali chlorides are plotted against composition in Figure 6. This figure also contains partial excess free energies taken from the emf investigations of Markov, et d.,' and of Neil, et aL6 The Journal of Physical Chemistry
It is apparent that the agreement between the two emf studies is far from satisfactory. As an aid in our assessment of the relative merit of the two sets of data, we have included in Figure 6 the excess free energies calculated for magnesium chloride-rich mixtures from the phase diagrams of Klemm and co-~orkers.1~*1~ These calculations are based on the known heat of fusion of magnesium chloride (10.3 kcal/mole).'* It is assumed that this quantity does not depend on temperature and that solid solubility is negligible. It will be noted that the agreement between the phase diagram values and the data of Neil, et al., is quite good. However, the results of Markov and coworkers differ significantly. These values therefore will not be considered in the present discussion. Figure 6 shows that for the two systems studied by X'eil, et al., there is extensive similarity between our own enthalpy data and the excess free energies. It accordingly may be concluded that the excess entropies in these two systems are not very large. This is true in particular for the mixtures involving sodium chloride, while those containing potassium chloride show somewhat greater differences. For the latter system the partial excess entropies for magnesium chloride a t about 800" have been evaluated and are plotted against mole fraction in Figure 7. While it is difficult to assess the error in these entropy data, it is believed that they correctly reflect the general shape of the excess entropy curve. Note especially the positive values of S E 1 f ~for , , Xygclz > 0.4 and the negative values for low magnesium chloride concentrations. Such a functional dependence of the partial entropy on composition corresponds to a fairly sharply defined local minimum in the integral entropy curve. I n the considered system, this minimum clearly occurs at or near 0.33. I n the partial enthe composition X N ~ C=I ~ thalpy curves, as in the corresponding free energies, =C0.33 I ~ is associated with an the composition X M M ~ inflection point. This is barely noticeable in the lithium-magnesium system, but becomes more and more well defined as the alkali ion increases in size. Qualitatively, the functional dependence of the partial quantities on composition near x M g C 1 2 = 0.33 may be accounted for in terms of the high degree of local order associated with this composition, compared to neighboring compositions. More quantitatively, this problem may perhaps be discussed by a suitable (16) W. Klemm and P. Weiss, 2. Anorg. Allgem. Chem., 245, 279 (1940). (17) W. Klemm, K. Beyersdorfer, and J. Oryschkewitsch, ibid., 256,
25 (1948). (18) National Bureau of Standards Circular 500, U. S. Government Printing Office, Washington, D. C., 1952.
THERMOCHEMISTRY OF BINARY HALIDEMIXTURES
I
I
I
I
I
1
I
I
I
I
3
0 t0.0
”
bN-0.4 0
c
-0.0 -I .2
-1.6 MgCI,
“4
0
0.2
0.4
0.6
0.0
KC I
Mole Fraction, X K C -
Figure 7 . Partial excess entropy of magnesium chloride in its liquid mixtures with potassium chloride. From the partial enthalpies derived in the present work and the excess free energies of Neil, et at.
modification of the statistical theory for nearly ordered solid compounds developed by Wagner and Schottkyl9 and by Ulander.% I n the considered case, the “compound” refers to the liquid mixture of composition AzMgC14,while the “degree of disorder” presumably may be related to the partial dissociation of the anionic species according to the equation MgC1d2-
Mg2+
+ 4C1-
However, from a chemical point of view it seems more natural to take this dissociation process as a starting point, as was done by Flood and Urnes4 in their discussion of the cryoscopic behavior of the alkali chloridemagnesium chloride systems. For potassium and rubidium chloride as solvents, Flood and Urnes found that the freezing point depressions up to X ~ g c 1=~ 0.25-0.30 can be accounted for quantitatively by the assumption that the solution is an ideal Temkin mixture21 of A+, MgC142-, and C1-, i.e., that all MgCl2 is complexed to form MgCI42-. I n sodium chloride, on the other hand, there are deviations from this simple picture. These deviations were attributed to the dissociation of MgC142- in the presence of the smaller sodium ion. A similar and still more pronounced deviation may be predicted for mixtures involving the even smaller lithium ion. For solutions rich in magnesium chloride, on the other hand, Flood and Urnes were unable to account
1255
for the cryoscopic behavior in terms of an ideal Temkin mixture, now assumed to contain the ions A+, Mg2+, MgC1d2-, and C1-, since there are too few chloride ions present to complex all magnesium ions. The difference between the magnesium- and alkali-rich melts may readily be understood in view of the concentration dependence of AHM indicated in Figure 1, and the observed dependence of the relative partial enthalpy of MgClz on composition. More recently, the existence of the complex species MgCld2- has been argued by Neil, et al., who have used their free energy data to estimate the magnitude of the complex dissociation constant. For solutions containing 20 mole % magnesium chloride in sodium chloride and potassium chloride, Neil gives dissociation constants, according to the equation given above, of and 1.8 X loW3,respectively, at 8002.3 X 825°.22 Using these values, and the ideal Temkin model, he goes on to calculate partial free energies for magnesium chloride over the complete range of liquid compositions. With respect to the functional dependence of the partial free energy on composition near X M ~ C = I0.33, ~ there is reasonable agreement between Neil’s calculated values and experiment. Thus it is indicated that in a qualitative way the thermodynamic properties of the alkali chloride-magnesium chloride mixed systems may be accounted for fairly well by the postulation of the single complex species MgCI42-. On the other hand, in a quantitative sense it undoubtedly is much too crude to assume a single, concentration-independent dissociation constant for each binary system. This is inconsistent both with the already mentioned analysis of the cryoscopic data and with the new enthalpy data reported in the present work. Acknowledgments. This work was supported by the National Science Foundation (Grants GP-1993 and GP-5015) and by the Office of Naval Research (Nonr2121 (11)). The work also has benefited from general facilities a t the Institute for the Study of Metals provided by the Advanced Research Projects Agency. (19) C. Wagner and W. Schottky, Z. Physik. Chem., B11, 163 (1930). (20) A. Olander, ibid., A165, 65 (1933). (21) M. Temkin, Acta Physicochim. URSS,20, 411 (1945). (22) These dissociation constants seem to be of a reasonable order of magnitude. In view of the partial heat data given in Figure 6, the corresponding dissociation constants for a cesium chloride medium should be of the order of 10-4 and for a lithium chloride medium 10-1. This estimate is based on the assumption OE c RE.
Volume 70, Number 4 April 1966
